We could always create some sort of high tech moonbase (like the one in Codename: Kids Next Door). Terrorists would have a blast trying to get up there. It would also be a haven from a possible World War 3 and the nuclear apocalypse that would follow.
Let's see, we could use solar powered boats, boats with wind sails, boats with oars...
A capital is always big city. Now if the capital of a country is about 0.5 - 2 million, then the capital of the world should be around 10-20 million. Now consider that the only non-explodable power source is solar, wind, water, or muscle power. Building a transport system for so many citizens and especialy tourists by the millions using those power sources, who, as you know, are not very productive, would need solar/wind farms by the square miles, daming a lot of rivers, or a world-wide lawsuit involving animal/human rights. Also the boats would need to be fast, so the cost would also rise and riding the currents would be out a question. The defensive navy by the island would have to be fueled. You would also have to build a military airport somewhere (the nearby island) so that the city and the navy would have to have protection, and running them not on fuel is out of the question. on land you have land streaching for miles in every direction so you could have protection for miles about. You would have to spend dollars by the trillions only because you wanted it on an island.
I know ima get a bomb dropped on me for this but I'd say Jerusalem. Yes I know it has to do with many religions and all but its also where most of us came from due to it being near Mesopotamia, also known as the Cradle to Civilization.
Actually the "world's stock market" is not in New York. This is a common misconception because many international companies are traded on the NYSE, however there are several markets. The NYSE is the largest stock exchanges in the world, however it is not the only one. It's importance is simply that American investors are much more vocal than their international counterparts, and widely covered in the media, hence continuing the misconception that it is the "world's market".
What we have in New York is simply one of many stock exchanges. These exchanges are places where you can buy and sell stock (portions of companies). There are exchanges in India, UK, Germany, Japan, Spain, and numerous other nations.
However for a world capitol to be a prudent or even successful occurrence we first need to reduce nationalism, expand democracy and freedoms to all corners of the globe and eliminate zealotry.
Haha good luck with that, your going to need it haha.
Personnally it would have to go between: - Jerusalem - I think this city because everyone would be welcome there, since it holds like ALL of the Religions there, it would be friendly to all + I'm a strong Christian
Avorne's Idea - But instead of taking by force or defending with force why not get it while in peace?